It has heretofore been proposed, for example as shown in U.S. Pat. No. 2,555,708, to form a cylindrical curl or roll on a sheet of material by forcing the sheet edgewise through a tangent slot in an otherwise closed cylindical die having a core member inside the die. However, with such a closed curling die apparatus, it is necessary to provide a core member extending the length of the curling die and to relatively move the sheet, die and core member in a direction axially of the die in order to separate the curled sheet from the die and core member. Such a closed curling die accordingly was not suitable for forming relatively long curls. It has also been proposed, as shown in U.S. Pat. Nos. 708,015 and 735,936 to use open curling dies having only a semi-cylindrical cavity. However, because of problems encountered in forming the initial portion of the curl using such open semi-cylindrical dies, it was necessary in such prior open curling dies to pre-bend or pre-curl the lead edge of the sheet into at least a portion of a cylinder, before feeding the same into the semi-cylindrical curling die. Such a two step operation for curling the sheet not only increased the amount of handling and time required to form a curl on the sheet but also made it difficult to form a smooth continuous curl free of discontinuities.